We've recently had some armoured electric cables put in underground (in a protective tube) for a hot tub, however it's had to be positioned running about 50cm parallel to a fence that I had wanted to plant some hedging and shrubs along this fence for privacy.... will this still be possible? Would the roots be a danger and make this a safety hazard or will the cables be fine protected in its tube?

The plants I had in mind were Red Robins, Conitus and Ceanothus.

I'm a very novice gardener, so any advice or recommendations on what best to do here would be much appreciated.

Contact your utility company and ask them.

If the wire is inside of conduit tubing, shouldn't be a problem... When I run wires across my planting areas, I try to use conduit... cut through enough live wires, eventually we start trying to protect them.

If the wires are inside a conduit designed to be buried, the roots should not be a problem. The potential problem is that someone might cut through the conduit while digging, maybe to plant something, or to put in a post or anything like that.

Armored inside of PVC conduit? I assume the circuit is GFI/GFCI protected. The roots shouldn't be a problem. You could always flag the path of the conduit so it doesn't get dug up inadvertently .